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Some Contributions to Filtering, Modeling and Forecasting of Heteroscedastic Time Series
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Heteroscedasticity (or time-dependent volatility) in economic and financial time series has been recognized for decades. Still, heteroscedasticity is surprisingly often neglected by practitioners and researchers. This may lead to inefficient procedures. Much of the work in this thesis is about finding more effective ways to deal with heteroscedasticity in economic and financial data. Paper I suggest a filter that, unlike the Box-Cox transformation, does not assume that the heteroscedasticity is a power of the expected level of the series. This is achieved by dividing the time series by a moving average of its standard deviations smoothed by a Hodrick-Prescott filter. It is shown that the filter does not colour white noise.

An appropriate removal of heteroscedasticity allows more effective analyses of heteroscedastic time series. A few examples are presented in Paper II, III and IV of this thesis. Removing the heteroscedasticity using the proposed filter enables efficient estimation of the underlying probability distribution of economic growth. It is shown that the mixed Normal - Asymmetric Laplace (NAL) distributional fit is superior to the alternatives. This distribution represents a Schumpeterian model of growth, the driving mechanism of which is Poisson (Aghion and Howitt, 1992) distributed innovations. This distribution is flexible and has not been used before in this context. Another way of circumventing strong heteroscedasticity in the Dow Jones stock index is to divide the data into volatility groups using the procedure described in Paper III. For each such group, the most accurate probability distribution is searched for and is used in density forecasting. Interestingly, the NAL distribution fits best also here. This could hint at a new analogy between the financial sphere and the real economy, further investigated in Paper IV. These series are typically heteroscedastic, making standard detrending procedures, such as Hodrick-Prescott or Baxter-King, inadequate. Prior to this comovement study, the univariate and bivariate frequency domain results from these filters are compared to the filter proposed in Paper I. The effect of often neglected heteroscedasticity may thus be studied.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University , 2010. , 34 p.
Keyword [en]
Heteroscedasticity, variance stabilizing filters, the mixed Normal - Asymmetric Laplace distribution, density forecasting, detrending filters, spectral analysis, the connection between financial data and economic growth
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:su:diva-38627ISBN: 978-91-7447-107-6 (print)OAI: oai:DiVA.org:su-38627DiVA: diva2:311616
Public defence
2010-06-04, hörsal 4, hus B, Universitetsvägen 10 B, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2010-05-11 Created: 2010-04-22 Last updated: 2010-06-16Bibliographically approved
List of papers
1. A Simple Heteroscedasticity Removing filter
Open this publication in new window or tab >>A Simple Heteroscedasticity Removing filter
2007 (English)Report (Other academic)
Abstract [en]

In this paper variance stabilizing filters are discussed. A new filter with nice properties is proposed which makes use of moving averages and moving standard deviations, the latter smoothed with the Hodrick-Prescott filter. This filter is compared to a GARCH-type filter. An ARIMA model is estimated for the filtered GDP series, and the parameter estimates are used in forecasting the unfiltered series. These forecasts compare well with those of ARIMA, ARFIMA and GARCH models based on the unfiltered data. The filter does not colour white noise.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2007. 27 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 1
Keyword
Economic growth, heteroscedasticity, variance stabilizing filters, the Hodrick-Prescott filter
National Category
Economics
Identifiers
urn:nbn:se:su:diva-21073 (URN)
Available from: 2010-04-23 Created: 2008-01-18 Last updated: 2010-04-23Bibliographically approved
2. On the Probability Distribution  of Economic Growth
Open this publication in new window or tab >>On the Probability Distribution  of Economic Growth
2008 (English)Report (Other academic)
Abstract [en]

Normality is often mechanically and without sufficient reason assumed in econometric models. In this paper three important and significantly heteroscedastic GDP series are studied. Heteroscedasticity is removed and the distributions of the filtered series are then compared to Normal, Normal Mixture and Normal - Asymmetric Laplace (NAL) distributions. NAL represents a skewed and leptokurtic distribution, which is in line with the Aghion and Howitt (1992) model for economic growth, based on Schumpeter's idea of creative destruction. Statistical properties of the NAL distributions are provided and it is shown that NAL competes well with the alternatives.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2008. 30 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 5
Keyword
The Aghion-Howitt model, asymmetric innovations, mixed Normal - Asymmetric Laplace distribution, Kernel density estimation, Method of Moments estimation
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-38646 (URN)
Available from: 2010-04-23 Created: 2010-04-23 Last updated: 2010-04-23Bibliographically approved
3. Density Forecasting of the  Dow Jones Stock Index
Open this publication in new window or tab >>Density Forecasting of the  Dow Jones Stock Index
2010 (English)Report (Other academic)
Abstract [en]

The distribution of differences in logarithms of the Dow Jones stock index is compared to the Normal (N), Normal Mixture (NM) and a weighted sum of a normal and an asymmetric Laplace distribution (NAL). It is found that the NAL fits best. We came to this result by studying samples with high, medium and low volatility, thus circumventing strong heteroscedasticity in the entire series. The NAL distribution also fitted economic growth, thus revealing a new analogy between financial data and real growth.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2010. 21 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 1
Keyword
Density forecasting, heteroscedasticity, mixed Normal - Asymmetric Laplace distribution, Method of Moments estimation, connection with economic growth
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-38647 (URN)
Available from: 2010-04-23 Created: 2010-04-23 Last updated: 2010-04-23Bibliographically approved
4. Comovements of the Dow Jones Stock Index and US GDP
Open this publication in new window or tab >>Comovements of the Dow Jones Stock Index and US GDP
2010 (English)Report (Other academic)
Abstract [en]

This paper explores the connection between Dow Jones industrial average (DJIA) stock prices and the US GDP growth. Both series are heteroscedastic, making standard detrending procedures, such as Hodrick-Prescott or Baxter-King, inadequate. The results from these procedures are compared to the results from heteroscedasticity corrected data, thus the effect of the neglected heteroscedasticity is measured. The analysis is mainly done in the frequency domain but relevant time domain results are also reported.

Place, publisher, year, edition, pages
Stockholm: Department of Statistics, Stockholm University, 2010. 29 p.
Series
Research Report / Department of Statistics, Stockholm University, ISSN 0280-7564 ; 2
Keyword
Spectral analysis, detrending filters, heteroscedasticity, the connection between stock prices and economic growth
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:su:diva-38648 (URN)
Available from: 2010-04-23 Created: 2010-04-23 Last updated: 2010-04-23Bibliographically approved

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